This paper describes new methods for the interpretation of microwave scatter from the sea. Rough-surface scattering theory has led to an integral equation for the echo voltage in terms of the joint height-slope probability density function (pdf). We have developed methods for the inversion of this equation that do not require the assumption of a model for either the ocean surface or the transmitted pulse. In addition they are far more efficient than traditional grid-search methods for model fitting. We have applied our methods to SEASAT data taken over Hurricane Fico. Statistical data analysis was performed to give the data covariance matrix and the correlation coefficient between successive waveforms and to trace the propagation of error through the inversion process to give statistical uncertainties in the derived parameters. The usual assumption of Rayleigh statistics is shown to be violated by the data, since the number of degrees of freedom increases linearly with power, independent of sea state; we conclude that this is an instrumental effect. We find that the waveforms are significantly correlated over distances of several kilometers at high sea states and suggest coherence of long ocean waves over these distances as the cause. We obtained waveheight higher-order parameters by least squares fitting of a Gram-Charlier model for probability densities to the calculated values. For averages over 160 km of sea, we obtain a mean surface height bias correction, significant waveheight, and height skewness parameter with standard deviations of 4.07, and 15%. In addition to this height bias correction easily removed form the data, we identify another sea-state-dependent height bias that can exceed 50 cm. That this exists in the data is proof that one must employ the joint heigh-slope pdf in the scattering model, and not merely the height pdf as conventionally used.